With the aid of an LED, which, for example, produces blue light and converts part of the blue light into yellow light by a suitable converter material, white light can be produced because of the resultant color mixing of the original blue light with the converted yellow light. A problem thereby arising is described in DE 199 18 370 A1 (U.S. Pat. No. 6,759,803). On account of different path lengths of light rays within a resin filling surrounding the LED, in which the converter material is contained, the yellow component may predominate in the overall radiation in the peripheral region of a blue element, whereas by contrast the blue component predominates in the middle. According to DE 199 18 370 A1, this problem is solved by creating a uniform path length of the omnidirectionally emitted light radiation by an appropriate shape of the resin filling, to be specific by a convex surface of the resin filling.